Run-Time Efficiency of Bilinear Model Predictive Control Using Variational Methods, With Applications to Hydronic Cooling

Abstract

Effective real-time execution of nonlinear model predictive control (NMPC) on embedded systems is significantly dependent on the controller formulation. This paper studies the effect of model structure and cost functions on the computation time of scalar bilinear NMPC using variational methods, with hydronic cooling applications. Two algebraically equivalent nonlinear model structures common in literature are primarily considered: a linear state equation with state-dependent control constraints and a bilinear state equation with time-invariant rectangular control constraints. Additionally, the effects of three cost function formulations are also considered: minimum-time, quadratic regulation, and efficient state constraints. Highfidelity computer simulations, hardware-in-the-loop testing, and experiments on a bench-scale hydronic cooling system are used to study sources of computational complexity, rates of convergence, initialization techniques, and overall effectiveness of the different models and costs. These results suggest that NMPC with bilinear state equations, minimizing pump power and a one-sided quadratic state cost, converges sufficiently fast and reliably. This presents an attractive alternative to the traditionally constrained linear quadratic regulator-based NMPC on embedded systems.

Model prediction of spatial non-cooperative target measurement information based on the Koopman operator

“…In the case of optical relative navigation measurement models based on sequence images, which are typical nonlinear models, current traditional solutions for prediction problems can be categorized into two approaches: One approach is to establish Wiener models 6 or bilinear models 7 for nonlinear systems. Through Wiener or bilinear models, the characteristics and nonlinear features of the system can be analyzed more deeply.…”